Description of Templates
Template Versions Available
How to Use the Standard Precision Template
Output
Bowker's Test of Symmetry
Pivot Tables
Contact Info
References

Description

A series of Microsoft Office Excel* templates were designed to automate the calculation of various measures of ageing precision, including percent agreement and the total coefficient of variance (CV, Chang 1982), plus generating both an age-bias plot and an age matrix table. These measures were recommended by Campana et al. (1995). In the standard template, symmetry is also tested with a Bowker's test (Hoenig et al. 1995) if the percent agreement drops below 90%.

These templates were created in Microsoft Office Excel 2003*. Please feel free to download and apply them as needed, and to share them with other interested parties. As of the release date, all these templates were correct to the best of my knowledge.

Templates are currently being tested in Microsoft Office Excel 2007*. Please use the Contact Info below to request these updates when they become available.

     Click on each filename to download the corresponding template.

The description that follows applies specifically to the standard template (Precision.xlt). The other templates are comparable, but cell positions can change from one template to another. Information on the Bowker's test applies only to the standard template.

Production (prod.) age is considered to be the first age attached to a given fish, obtained while the age reader is working with the entire set of samples (survey, commercial quarter, etc.). Ages obtained while re-ageing fish from the precision subsample are labeled 'test ages.' (Note: In the Accuracy template, reference (ref.) age is used to indicate the known or consensus age for each fish.)

Note: All data shown in red on the template should be replaced.

Step 1: First, the two sets of ages must be entered in columns A (prod. age) & B (test age), starting at row 36. Overwrite the sample ages already listed. Fish which are omitted in either ageing run may be listed in the table at J36, but should not be included in this section. Blank lines in the age data must also be avoided, as these can artificially reduce the total CV.

Note: Do not change the first 34 rows of 'space-keeper' ages. They are included to ensure that the Pivot Tables list all ages, which in turn allows other calculations to refer to the correct locations.

Step 2: Once all ages are entered, the calculations in columns C-E (starting at row 36) must be copied downward to the last age pair. The computer sometimes does this automatically, depending on how the ages are entered.

These columns calculate the CV for each fish (indicated by the subscript 'j'). Multiple columns were used in order to simplify the equations. The column values are:

C, the average age, X_j;
D, the sum of the squared differences (SSD) between each age and X_j; and
E, CV_j, the square root of the SSD_j divided by X_j.

For fish for which both ages are zero, the 'IF' statement in column E resets the CV_j to zero to avoid an error message. This could convert blank lines in your data to artificial CV_j values of zero. To remove any blank lines, you can run the 'sort' function on both columns of ages before copying the calculations. (Note: On the 30- and 50-year templates, any age-0 fish in columns A or B will generate a '#ZERO!' message in column E, and the Pivot Tables will not work properly.)

Step 3: Move to the upper right portion of the template. Pivot Table 1 starts at cell AN1; Pivot Table 2 starts at AN23. Both Pivot Tables must be refreshed. This can be done simply by right-clicking within each Pivot Table, and selecting the 'Refresh Data' option. See below for more details on Pivot Table layout.

Note: These tables begin in Column AZ for the 25-year template, Column BA for the 30-year template, and Column CF for the 50-year template.

Step 4: At the top of Columns H-N, the labels should be updated, including:

H1, the sample type (survey, commercial, etc.) and year the fish were captured;
H2, what is compared (repeated readings of the same fish/comparison between two readers);
N1, the species name;
N2, the date the exercise was completed; and
N3, the name of the age reader.

Add other information, such as stock area, as appropriate.

Step 5: Save the file to a new, distinctive filename before printing. A file name which incorporates species, sample source, and age reader is recommended. For example, "SJS_HD_200303_GOM.xls" would refer to an exercise which I completed on haddock collected on the 200303 survey in the Gulf of Maine.

Output

The printed data (H1-AL43) show the sample size, total CV (expressed as a percentage), percent agreement, and Bowker's test results (if appropriate; see below). A breakdown of the average test age for each production age (with measures of variation) is shown in both table form and in the age-bias plot. An age matrix table is included, as well. The header lists the document name and the date printed.

Click on the table to open in a new window. 

For much of the printout, zeroes are not shown. Disregard any "#DIV/0!" and "#NUM!", as all ages may not be adequately represented in your sample. Do not attempt to remove these from the template, as the calculations in those cells may be needed in another precision exercise.

Note: The output for the 50-year template is arranged differently, but contains the same elements.

In the standard template, the cells below the printout (J45-AJ85) are used in calculating the Bowker's test (Hoenig et al. 1995). This considers only the samples for which the age was not agreed upon. Comparisons are made on the diagonal, i.e. fish with ages of (1, 2) are compared with fish having ages of (2, 1).

Cells S46-AJ64 calculate the chi-squared value for each diagonal pair of ages, based on the data in the age matrix table. Cells S67-AJ85 indicate which of these pairs include actual fish; this total (cell K59) is the number of degrees of freedom for the test. In cells K46-K55, the chi-squared values are summed for each difference between the two ages (i.e. 1 year, 2 years, etc.), with an overall total in cell K58. Differences of 10 or more years are combined in cell K55, and broken out in cells K65-K71. Hopefully, there will be few disagreements of this magnitude.

The results of the Bowker's test are reported in the printout only if the percent agreement is below 90%. A significance level of P<0.05 is used to distinguish between significance (**) and non-significance (n/s). If the test is not reported, these cells (P6-P9) contain 'N/A' for 'not applicable.'

Note: The standard precision template is the only one in this set which incorporates a Bowker's test. It is not applicable to an accuracy exercise against known-age samples, nor are the necessary calculations conducive to inclusion on the precision templates for long-lived species. If a symmetry test is needed for older fish, use Symmetry50yr.xlt.

 

Pivot Table 1

The upper Pivot Table (AN1-AR20) calculates the Total CV and statistics for the test ages at each production age. The Pivot Table refers to Columns A, B, and E. Line 21 is included to make necessary adjustments to the Pivot Table results, by accounting for blank spaces in A2-B35. Mean CV is later calculated as (Sum of Total CVs)/N from cells AQ21 and AR21. Part of this table is mirrored in cells M13-N30 on the printout, as well.

Use of production age as the basis for these calculations is arbitrary and is not meant to indicate that either set of ages is more accurate. Either set could be used here and as the x-axis in the age bias plot.

Pivot Table 2

The lower Pivot Table (AN23-BG43) is the basis for the age frequency table in the printout, and the source of counts of fish and percent agreement values by age. It refers to columns A and B only. Again, line 44 is present to adjust the totals because of blank spaces at the top of Columns A and B.

Contact Info

Please contact Sandy Sutherland (Sandy.Sutherland@noaa.gov) if you need any assistance with these templates, or would like advice in developing your own.

References

Campana, S. E., Annand, M. C., and McMillan, J. I. (1995). Graphical and statistical methods for determining the consistency of age determinations. Trans. Am. Fish. Soc. 124, 131-8.

Chang, W. Y. B. (1982). A statistical method for evaluating the reproducibility of age determination. Can. J. Fish. Aquat. Sci. 39, 1208-10.

Hoenig, J. M., Morgan, M. J., and Brown, C. A. (1995). Analysing differences between two age determination methods by tests of symmetry. Can. J. Fish. Aquat. Sci. 52, 364-8.

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